Carry Trades and Global Foreign Exchange Volatility

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1 Carry Trades and Global Foreign Exchange Volatility Lukas Menkhoff Leibniz Universität Hannover Maik Schmeling Leibniz Universität Hannover Lucio Sarno CASS Business School and CEPR Andreas Schrimpf Aarhus University and CREATES 1 / 53

2 Motivation We study the risk-return profile of carry trades in FX markets: Borrow money in low interest rate currencies (e.g. JPY). Invest in high interest rate currencies (e.g. AUD). Uncovered interest parity (UIP) suggests that changes in the exchange rates will eliminate this interest rate margin. However, this mechanism fails on a grand scale: forward premium puzzle (Hansen, Hodrick 1980, 1983; Fama, 1984). considerable returns to currency speculation (e.g. Lustig, Verdelhan, 2007; Burnside et al., 2008, 2009; Lustig, Roussanov, Verdelhan, 2009). This paper: cross-section of carry trade returns can be explained by exposure to global FX volatility risk. 2 / 53

3 Preview: Excess returns and volatility states Figure : Excess Returns on Carry Trade (H/L) Portfolio and Volatility (a) All Countries (b) Developed Countries Average excess returns (in % p.a.) Average excess returns (in % p.a.) Low 2 3 High Distribution of Global FX Volatility -10 Low 2 3 High Distribution of Global FX Volatility 3 / 53

4 Motivation for volatility risk Intertemporal CAPM (ICAPM): According to ICAPM theory (Merton, 1973; Campbell, 1993), investors are concerned about deteriorations of the investment opportunities set. Chen (2003) and Ang et al. (2006): volatility as a state variable affecting the evolution of future investment opportunities (unexpected) market volatility as a systematic risk factor. Implications related to Coskew (Harvey and Siddique, 1999), non-linear pricing kernels (Dittmar, 2005). This paper takes a cross-sectional asset pricing / SDF route to explain the returns to currency speculation. 4 / 53

5 Recent literature Lustig and Verdelhan (2007) were the first to look at a cross-section of carry trade portfolios offer a consumption-based explanation. Brunnermeier et al. (2008): currency crashes and funding liquidity. Burnside et al. (2008, 2009): role of Peso problems, standard risk factors fail to explain returns to currency speculation. Lustig, Roussanov, and Verdelhan (LRV, 2009) study an empirically derived slope factor to price the cross-section of currency returns Two important factors: a level (Dollar risk) and a slope (HML FX ) factor. 5 / 53

6 Overview of main results 1 Global FX volatility accounts for the cross-sectional spread in expected carry trade returns. 2 Sorting currencies by their exposure to past volatility innovations reproduces the cross-section of carry trade portfolios. 3 Volatility dominates liquidity risk in horse races. suggests systematic results across asset classes (e.g. Ang et al. 2006; Bandi et al. 2008; Da, Schaumburg, 2009). 4 Proposed risk factor is also helpful for pricing other assets as well. Overall, the results in this paper suggest that there is a meaningful risk-return relation in the FX market. 6 / 53

7 Data We use data on forward rates (f ) and spot rates (s) from BBI and Reuters/WMF (via Datastream). Total sample consists of 48 countries. Countries We also use a smaller sample of 15 developed countries. Sample period: 11/ /2009 (monthly). 7 / 53

8 Currency excess returns We calculate excess returns for a US investor. USD excess return to investing in foreign currency k: rx k t+1 = i k t i US t s k t+1 s k t : log spot exchange rate (foreign currency per one unit USD) (s increases USD appreciates). Since the (log) forward discount ft k st k it k it US rx k t+1 = f k t s k t+1 (CIP): 8 / 53

9 Currency portfolios Sort currencies into five portfolios based on (lagged) forward discounts (i.e. interest rate differentials): Portfolio 1: 20% of all currencies with lowest forward discounts i.e. lowest interest rates relative to the US.... Portfolio 5: 20% of all currencies with highest forward discounts i.e. highest interest rates. Monthly re-balancing; transaction-cost adjusted returns. TC Two important portfolios (LRV 2009): Average of five portfolios: Dollar Risk -factor (DOL) Portfolio 5 minus Portfolio 1: Carry Trade -factor (HML FX ) 9 / 53

10 Currency portfolios: Excess returns All countries (with b-a) Portfolio Avg. H/L Mean Sharpe Ratio Developed countries (with b-a) Portfolio Avg. H/L Mean Sharpe Ratio Notes: The sample period is 11/ /2009, annualized monthly returns 10 / 53

11 A parsimonious linear two-factor SDF Chen (2003) extends discrete-time ICAPM of Campbell (1993,1996) by time-varying volatility ICAPM covariance with innovations to aggregate vol. as additional source of risk. Negative volatility risk premium: High unexpected volatility ( bad state of the world). Assets covarying positively with market vol. innovations provide a good hedge low expected return. A parsimonious two-factor SDF in line with the literature on equity markets (Ang et al. 2006): m t+1 = 1 b 1 r e m,t+1 b 2 V t+1 11 / 53

12 FX Volatility proxy σ FX t = 1 T t τ T t [ ( ) ] r k τ k K τ K τ r k τ return of currency k on day τ (daily spot rate change s τ ). K τ number of available currencies on day τ. T t number of trading days in month t. Average of daily absolute returns (across countries), averaged over the month. According to the ICAPM, only unexpected volatility should be priced - volatility innovations obtained from a simple AR(1). Carry trades perform poorly when global FX vol. is high: Corr( σ FX t, HML FX,t ) / 53

13 Carry trades and global FX volatility Cumulative Carry Trade Returns Cumulative log excess return (in % p.a.) Developed countries All countries Global FX Volatility 1.25 Global FX volatility Volatility Volatility innovations / 53

14 Empirical methodology: GMM Basic no-arbitrage pricing equation E[m t+1 rx i t+1] = 0, i = 1,..., N with a linear SDF m t = 1 b (h t µ). Estimation via GMM g(z t, θ) = [1 b (h t µ)] rx t h t µ (h t µ)(h t µ) Σ h We report b, implied λs, cross-sectional R 2 s, and HJ-dist with simulated p-values. Further methodological details 14 / 53

15 Overview of major results 1 Volatility risk captures the spread in cross-sectional carry trade excess returns. 2 Sorting currencies on past volatility-betas reproduces the cross-section of carry trade portfolios. 3 Volatility risk dominates in horse races with liquidity proxies. 15 / 53

16 Volatility risk: Cross-sectional asset pricing tests Factor Betas All countries (with b-a) PF α DOL VOL R Factor Prices and Loadings All countries (with b-a) GMM DOL VOL R 2 HJ-dist b s.e. (0.05) (2.96) (0.79) λ s.e. (0.25) (0.03) FMB DOL VOL χ 2 SH χ 2 NW λ (Sh) (0.15) (0.02) (0.72) (0.82) (NW) (0.12) (0.03) 16 / 53

17 Volatility risk: Cross-sectional asset pricing tests Fitted mean excess returns (in %) P P3 P4 2 1 P2 0-1 P Realized mean excess returns (in %) 17 / 53

18 Volatility risk: Factor-mimicking portfolio Global FX volatility innovations are not a traded risk factor (unlike market excess return in a standard CAPM or LRV s HML FX ). We also build a factor-mimicking portfolio for the volatility factor by projecting volatility innovations on the five currency portfolios: This yields a factor-mimicking portfolio: rx FM t+1 = 0.202rx 1 t rx 2 t rx 3 t rx 4 t rx 5 t+1 Average return: rx FM t+1 = 0.107% p.m. ( 1.3% p.a.). Advantages: Tradable risk factor. Check for plausibility of prices of risk. 18 / 53

19 Volatility risk: Factor mimicking portfolio Results Panel A: Factor Prices and Loadings All countries (with b-a) GMM DOL VOL FM R 2 HJ-dist b s.e. (0.03) (0.23) (0.64) λ s.e. (0.15) (0.03) FMB DOL VOL FM χ 2 SH χ 2 NW λ (Sh) (0.13) (0.02) (0.60) (0.20) (NW) (0.12) (0.02) Factor price estimate for the FM portfolio: -1.22% p.a., close to the average return p.a. on the FM PF. 19 / 53

20 Volatility risk: Factor risk price FX option markets JP Morgan data on FX options, maturity one month. 29 currencies quoted against the USD, sample period: How does our factor risk price estimate compare to estimates from option markets? Build a zero-beta straddle portfolio (long calls, long puts equal weights) in the spirit of Coval/Shumway (2002) Loads on volatility risk but not market risk. Average return on the straddle portfolio -1.2% p.a. Close to our estimates based on the FM PF. Close in magnitude to factor risk price for stock markets of -1% p.a. reported by Ang et al. (2006) 20 / 53

21 Volatility risk: Beta sorts Sort currencies into five portfolios based on their past betas with global FX vol. innovations, 36 months rolling window. All countries Portfolio Avg. H/L Mean Sharpe Ratio pre-f. f s post-f. f s Currencies with low vol-betas (PF 1) low payoffs in times of high vol. innovations: high excess returns and high f s. Currencies with high vol-betas (PF 5) hedge against vol. risk: low excess returns and low f s. Carry Trade selects currencies subject to high volatility risk. 21 / 53

22 Volatility versus liquidity risk (Il-)Liquidity proxies Global foreign exchange bid-ask spreads: ψ FX t = 1 T t τ T t [ k K τ ( ) ] ψ k τ TED spread: 3M interbank rate (LIBOR) minus 3M T-Bill rate (Brunnermeier, Nagel, Pedersen, 2008). U.S. stock market liquidity measure (Pastor/Stambaugh, 2003). K τ FX vol. is correlated with illiquidity proxies Correlations 22 / 53

23 Volatility versus liquidity risk: Liquidity risk Example: Bid-ask spreads Panel A: Factor Prices and Loadings Global bid-ask spreads All countries (with b-a) Developed countries (with b-a) GMM DOL BAS R 2 HJ-dist GMM DOL BAS R 2 HJ-dist b b s.e. (0.05) (26.48) (0.16) s.e. (0.03) (22.63) (0.36) λ λ s.e. (0.24) (0.01) s.e. (0.21) (0.01) 23 / 53

24 Volatility versus liquidity risk: Horse races Panel A: Volatility and global bid-ask spreads GMM DOL BAS VOL R 2 HJ-dist b s.e. (0.07) (36.08) (4.24) (0.82) λ s.e. (0.31) (0.02) (0.04) Panel B: Volatility and TED spread GMM DOL TED VOL R 2 HJ-dist b s.e. (0.05) (2.94) (3.28) (0.66) λ s.e. (0.25) (0.24) (0.03) Panel C: Volatility and P/S liquidity measure GMM DOL PS VOL R 2 HJ-dist b s.e. (0.07) (10.36) (3.82) (0.65) λ s.e. (0.29) (0.04) (0.04) 24 / 53

25 Overview of further results 1 Extreme observations: winsorized series and estimation by empirical likelihood approach. 2 Volatility risk ( σ FX ) is related, but not equivalent to the carry trade factor HML FX. 3 Our volatility risk factor is also priced in other cross-sections: FX momentum, U.S. equity momentum, U.S. corporate bonds and individual FX returns. 4 Further assets (FX options, int. bond portfolios) and more robustness tests. 25 / 53

26 Rare events Impact of extreme observations? GMM treats observations symmetrically. Empirical likelihood Information in extreme observations (endogeneously) receives different weight than normal observations. Attractive estimation approach in the presence of rare events or peso problems (Ghosh/Julliard 2008). Effect on factor risk prices? 26 / 53

27 Extreme observations Empirical Likelihood EL estimates Panel A: All countries Blockwise EL estimates b DOL b VOL λ DOL λ VOL b DOL b VOL λ DOL λ VOL coeff coeff s.e. (0.05) (2.52) (0.24) (0.03) s.e. (0.05) (2.54) (0.27) (0.03) OIR-Test 1.33 OIR-Test 3.37 p-value (0.72) p-value (0.34) EL estimates Panel B: Developed countries Blockwise EL estimates b DOL b VOL λ DOL λ VOL b DOL b VOL λ DOL λ VOL coeff coeff s.e. (0.04) (3.09) (0.21) (0.03) s.e. (0.04) (3.08) (0.24) (0.04) OIR-Test 0.76 OIR-Test 5.55 p-value (0.86) p-value (0.14) 27 / 53

28 Global FX volatility innovations and HML FX A non-traded factor cannot beat a (return-based) factor mimicking portfolio factor in a horse race (Cochrane 2005). A level playing field: Horse races between (return-based) VOL FM and HML FX. HML FX (2nd PC of CT returns) and VOL FM no clear winner (some multi-collinearity). Res1 Orthogonal component of HML FX does not contain explanatory power once considered jointly with VOL FM. Res2 Both global FX vol. risk and HML FX are powerful factors to explain the cross-section of FX risk premia. 28 / 53

29 Other assets: FX momentum, U.S. corporate bonds 5 FX momentum portfolios (sorted on returns over past 12 months), 11/ / corporate bond portfolios (AAA-BA), duration-adjusted as in Da/Schaumburg (2009), 04/ / Currency Momentum Portfolios US corporate bonds GMM DOL VOL R 2 HJ-dist GMM DOL VOL R 2 HJ-dist b b s.e. (0.05) (4.69) (0.10) s.e. (0.34) (8.38) (0.81) λ λ s.e. (0.27) (0.05) s.e. (1.31) (0.08) FMB DOL VOL χ 2 SH χ 2 NW FMB DOL VOL χ 2 SH χ 2 NW λ λ (Sh) (0.15) (0.03) (0.08) (0.00) (Sh) (1.08) (0.04) (0.75) (0.89) (NW) (0.15) (0.04) (NW) (1.30) (0.07) 29 / 53

30 Other assets: U.S. equity momentum 10 U.S. equity momentum portfolios (K. French s website). US equity momentum GMM DOL VOL R 2 HJ-dist b s.e. (0.54) (7.07) (0.01) λ s.e. (2.38) (0.07) FMB DOL VOL χ 2 SH χ 2 NW λ (Sh) (1.84) (0.05) (0.11) (0.16) (NW) (2.27) (0.06) HMLFX Traditional AP Models 30 / 53

31 Other assets: Individual currencies DOL VOL HML FX R 2 λ t-stat [2.08] [-3.19] BS p-val (0.25) (0.05) (0.01) λ t-stat [2.40] [2.67] BS p-val (0.16) (0.12) (0.79) λ t-stat [2.01] [-2.84] [1.09] BS p-val (0.23) (0.08) (0.51) (0.01) 31 / 53

32 FX Options JP Morgan data on FX options, maturity one month. 29 currencies quoted against the USD, sample period: Quoted implied volatilities for Calls and Puts, different moneyness (ATM, 25-Delta, 10-Delta). IV patterns for portfolios sorted on lagged forward discounts (f-s) and lagged volatility betas. Results Estimation on a cross-section of portfolio returns on FX option strategies. 32 / 53

33 FX Options: Cross-sectional asset pricing tests 12 option portfolios (risk reversals, bull spreads and bear spreads). 12 Option portfolios GMM DOL VOL R 2 HJ-dist b s.e. (0.08) (5.20) (0.38) λ s.e. (0.44) (0.04) FMB DOL VOL χ 2 SH χ 2 NW λ (Sh) (0.20) (0.02) (0.16) (0.68) (NW) (0.19) (0.03) FX Opt. 33 / 53

34 FX Options: Cross-sectional asset pricing tests 12 option portfolios (risk reversals, bull spreads and bear spreads). 12 Option portfolios GMM DOL VOL R 2 HJ-dist b s.e. (0.08) (5.20) (0.38) λ s.e. (0.44) (0.04) FMB DOL VOL χ 2 SH χ 2 NW λ (Sh) (0.20) (0.02) (0.16) (0.68) (NW) (0.19) (0.03) FX Opt. 34 / 53

35 More robustness tests Different proxies for aggregate volatility: Country weights. Implied volatility: CBOE VIX index and JP Morgan FX VIX. IV Longer maturities. Bonds Potential EIV problems due to pre-estimation of vol. innovations can be ruled out (GMM System approach). Coskewness measure of Harvey/Siddique no monotone patterns. Other base currencies (GBP, CHF, JPY), i.e. other investors. Sub-samples analysis. Non-linearities. 35 / 53

36 Conclusions 1 Volatility risk matters for explaining carry trade risk premia. High interest rate currencies ( investment currencies ) perform particularly poorly during times of high (unexpected) volatility. Low interest rate currencies ( funding currencies in the carry trade) provide a hedge against volatility innovations. 2 Our results are in line with results for other asset classes: Cross-sections of stock returns (e.g. Ang et al., 2006), stock options and corp. bonds (Da, Schaumburg, 2009). Volatility risk dominates proxies for market (il)liquidity. 3 Many more results indicating that risk premia in FX markets reflect compensation for volatility risk. Meaningful risk-return relation in the FX market. 36 / 53

37 Sample countries Australia Austria Belgium Brazil Bulgaria Canada Croatia Cyprus Czech Rep. Denmark Egypt Euro area Finland France Germany Greece Hong Kong Hungary India Indonesia Ireland Israel Italy Iceland Japan Kuwait Malaysia Mexico Netherlands N. Zealand Norway Philippines Poland Portugal Russia Saudi Arabia Singapore Slovakia Slovenia S. Africa South Korea Spain Sweden Switzerland Taiwan Thailand Ukraine U.K. Total sample consists of 48 countries. Developed country sample: 15 countries highlighted in red Back 37 / 53

38 Other base currencies: FX volatility proxy Global FX Volatility Global FX Volatility Global FX Volatility Back 38 / 53

39 Currency excess returns Transaction costs Long position (sell USD forward in t, buy spot USD in t + 1): rx l t+1 = f b t s a t+1 Short position (buy USD forward in t, sell spot USD in t + 1): rx s t+1 = f a t + s b t+1 Back 39 / 53

40 Volatility versus liquidity risk: Correlations Correlation coefficients VOL BAS TED -PS VOL BAS TED PS Back 40 / 53

41 Volatility versus liquidity risk: Liquidity risk Panel A: Factor Prices and Loadings Global bid-ask spreads All countries (with b-a) Developed countries (with b-a) GMM DOL BAS R 2 HJ-dist GMM DOL BAS R 2 HJ-dist b b s.e. (0.05) (26.48) (0.16) s.e. (0.03) (22.63) (0.36) λ λ s.e. (0.24) (0.01) s.e. (0.21) (0.01) Panel B: Factor Prices and Loadings TED spread All countries (with b-a) Developed countries (with b-a) GMM DOL TED R 2 HJ-dist GMM DOL TED R 2 HJ-dist b b s.e. (0.07) (3.35) (0.53) s.e. (0.04) (2.06) (0.16) λ λ s.e. (0.30) (0.28) s.e. (0.24) (0.17) Panel C: Factor Prices and Loadings Pastor/Stambaugh liquidity measure All countries (with b-a) Developed countries (with b-a) GMM DOL PS R 2 HJ-dist GMM DOL PS R 2 HJ-dist b b s.e. (0.05) (8.29) (0.09) s.e. (0.04) (9.05) (0.94) λ λ s.e. (0.22) (0.03) s.e. (0.23) (0.03) Back 41 / 53

42 Empirical methodology The baseline SDF specification is given as A few further details: m t+1 = 1 b DOL (DOL t+1 µ DOL ) b VOL σ FX t+1. Estimation by pre-specified weighting matrix, equal weights for the test asset returns. HAC standard errors Newey-West with optimal lag selection by Andrews (1991). Factor risk prices λ backed out from the SDF slope parameters. We also report results from traditional FMB OLS two-pass regressions (incl. Shanken adjustments) i.e. beta-pricing framework. Back 42 / 53

43 ICAPM motivation of volatility risk Asset pricing in the discrete-time ICAPM (Campbell, 1993/1996 and extended by Chen 2003) E t ( r e i,t+1 ) + V ii,t 2 = γv im,t + (γ 1) V ih,t (γ 1)2 V iν,t 2 Three sources of risk premia: 1 V im,t Cov t ( r e i,t+1, r m,t+1 ), rm,t+1 is the market return. 2 V ih,t Cov t ( r e i,t+1, r h,t+1 ), rh,t+1 (E t+1 E t) j =1 ρj r m,t+1+j (changes in forecasts of future market returns). ( ) 3 V iν,t Cov t r e i,t+1, r ν,t+1, r ν,t+1 (E t+1 E t) j =1 ρj Var t+j (r m,t+j +1 + r h,t+j +1) (changes in forecasts of future market variances). Back 43 / 53

44 Horse-Races Interpretation A non-traded factor cannot beat a (return-based) factor mimicking portfolio factor in a horse race (e.g. Cochrane 2005). A level playing field: Horse races between the (return-based) VOL FM and HML FX. HML FX (essentially the second PC of CT returns) and VOL FM no clear winner (some multi-collinearity). Orthogonal component of HML FX does not contain explanatory power once included jointly with VOL FM. Individual currencies, economic magnitude of pricing errors: points towards an important role of volatility risk. Both HML FX and global FX vol. risk are powerful factors to explain the cross-section of FX risk premia. Back 44 / 53

45 Global FX volatility innovations and HML FX A non-traded factor can never beat a (return-based) factor mimicking portfolio in a horse race (e.g. Cochrane 2005). A level playing field: Horse races between (return-based) vol. innovations factor mimicking portfolio VOL FM and HML FX. Panel A: Volatility innovations and HML FX GMM DOL VOL HML FX R 2 HJ-dist b s.e. (0.06) (6.06) (0.07) (0.63) λ s.e. (0.27) (0.06) (0.33) Panel B: Factor-mimicking portfolio and HML FX GMM DOL VOL FM HML FX R 2 HJ-dist b s.e. (0.05) (1.52) (0.09) (0.69) λ s.e. (0.18) (0.01) (0.27) Back 45 / 53

46 Global FX volatility innovations and HML FX HML FX ( 2nd PC of CT returns) and VOL FM are strongly related multicollinearity issues when considering both at the same time. orthogonalizing VOL FM and HML FX against each other. Panel C: Factor-mimicking portfolio (orth.) and HML FX GMM DOL VOL Orth. FM HML FX R 2 HJ-dist b s.e. (0.04) (4.34) (0.03) (0.46) λ s.e. (0.16) (0.01) (0.24) Panel D: Factor-mimicking portfolio and HML FX (orth.) GMM DOL VOL FM HML Orth. FX R 2 HJ-dist b s.e. (0.04) (0.27) (0.06) (0.51) λ s.e. (0.19) (0.04) (1.09) Back 46 / 53

47 Other test assets: Individual currencies Mean excess return (in %) UAH BRL BGN SKK GBP HKD MYR ISK KRW EUR Volatility beta Notes: This figure cross-plots individual currencies volatility betas (horizontal axis) against mean excess returns (vertical axis). The red line shows the linear relation between betas and returns from a robust regression of returns on betas. Returns and betas for each currencies are calculated over the full available sample for that currency. Back 47 / 53

48 Implied volatility indices Factor Betas JPM G-7 Currency VIX S&P 500 VIX PF α DOL VIX R 2 PF α DOL VIX R (0.09) (0.06) (0.06) (0.09) (0.05) (0.02) (0.07) (0.05) (-0.16) (0.06) (0.04) (-0.02) (0.07) (0.05) (0.08) (0.06) (0.04) (0.02) (0.07) (0.05) (0.08) (0.06) (0.04) (0.02) (0.13) (0.10) (0.14) (0.12) (0.07) (0.03) Back 48 / 53

49 FX Option Portfolios Risk Reversals: long 25-Delta Put, short 25-Delta Call Bull spreads: long ATM Call, short 25-Delta Call Bear spreads: long ATM Put, short 25-Delta Put 4 portfolios for each strategy depending on lagged forward discount. Back 49 / 53

50 Other test assets and canonical models of equity pricing 10 U.S. equity momentum portfolios. Traditional asset pricing models (CAPM, Fama-French 3-factor model). Factor Prices and Loadings US stock momentum: CAPM US stock momentum: 3-factor model GMM MKTRF R 2 HJ-dist GMM MKTRF SMB HML R 2 HJ-dist b b s.e. (0.02) (0.00) s.e. (0.04) (0.18) (0.22) (0.02) λ 0.81 λ s.e. (0.36) s.e. (0.43) (1.25) (1.52) FMB MKTRF χ 2 SH χ 2 NW FMB MKTRF SMB HML χ 2 SH χ 2 NW λ λ (Sh) (0.27) (0.00) (0.00) (Sh) (0.28) (0.84) (0.98) (0.03) (0.01) (NW) (0.30) (NW) (0.29) (1.14) (1.42) Back 50 / 53

51 Other assets: HML FX 5 Currency Momentum Portfolios GMM DOL HML FX R 2 HJ-dist b s.e. (0.04) (0.05) (0.06) λ s.e. (0.16) (0.42) US stock momentum GMM DOL HML FX R 2 HJ-dist b s.e. (1.72) (0.85) (0.00) λ s.e. (7.13) (5.46) US corporate bonds GMM DOL HML FX R 2 HJ-dist b s.e. (0.29) (0.49) (0.01) λ s.e. (1.21) (3.58) Back 51 / 53

52 Other assets 5 portfolios of international bonds of different maturities sorted on redemption yield ( bond carry trade ). FX momentum portfolios (sorted on returns over past 12 months). 5 International Bond Portfolios 5 Currency Momentum Portfolios GMM DOL VOL R 2 HJ-dist GMM DOL VOL R 2 HJ-dist b b s.e. (0.04) (5.57) (0.07) s.e. (0.05) (4.69) (0.10) λ λ s.e. (0.31) (0.05) s.e. (0.27) (0.05) FMB DOL VOL χ 2 SH χ 2 NW FMB DOL VOL χ 2 SH χ 2 NW λ λ (Sh) (0.21) (0.03) (0.06) (0.12) (Sh) (0.15) (0.03) (0.08) (0.00) (NW) (0.16) (0.05) (NW) (0.15) (0.04) Back 52 / 53

53 FX Options IV patterns across portfolios Panel A: Carry Trade Portfolios Portfolio (low f-s) (high f-s) Delta Put 10-Delta Call [-3.91] [1.47] [1.77] [5.50] [9.47] [10.11] Panel B: Portfolios based on Volatility Betas Portfolio (low beta) (high beta) Delta Put 10-Delta Call [4.99] [4.00] [1.67] [0.52] [-0.56] [-3.75] High risk currencies (high f-s, low vol beta): higher IVs for puts than for calls Portfolio insurance for these high risk currencies is expensive. Back 53 / 53

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